STOCHASTICS WITH APPLICATIONS Seminar

 

PROGRAM

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Predavanja možete pratiti i online putem MITEAM stranice seminara Stohastika sa primenama:
https://miteam.mi.sanu.ac.rs/asset/n4AMxqgneB2qxFuT2

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Plan rada seminara Stohastika sa primenama za DECEMBAR 2025.

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Četvrtak, 04.12.2025. u 11:15, Online
Michael Oberguggenberger, University of Innsbruck, Austria
COLOMBEAU SOLUTIONS TO HYPERBOLIC SYSTEMS WITH RANDOM FIELD COEFFICIENTS
This talk addresses linear hyperbolic systems in one space dimension with random field coefficients. In many applications, a low degree of regularity of the paths of the coefficients is required, which is not covered by classical stochastic analysis. For this reason, we place our analysis in the framework of Colombeau algebras of generalized functions. Starting with a short recall of Colombeau's theory of generalized functions, we present a new characterizations of Colombeau stochastic processes and establish existence and uniqueness of solutions in this framework.
Three selected applications of the theory will be elaborated: The first one is to wave and transport equations on a curve, viewed as a Riemannian manifold, and perturbed by a random process with continuous paths of locally infinite length. The second application is to transport equations with drift perturbed by a white noise in time. The third application is to the linear wave equation with additive noise. In all cases, we compute the limiting behavior of the Colombeau trajectories and determine the relations to classical weak solutions, when the latter exist’

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Četvrtak, 18.12.2025. u 11:15, Online
Maja Obradović, Prirodno-matematički fakultet, Niš
A CLASS OF NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH TIME-DEPENDENT DELAY AND Θ-EULER-MARUYAMA METHOD (Θ ∈ (1/2,1))
Subject of consideration is the θ-Euler-Maruyama method (θ ∈ (1/2 ,1)) for a class of neutral stochastic differential equations with time-dependent delay. The theta method is defined such that, in general case, it is implicit in both drift coeffcient and neutral term. Sufficient conditions of the a.s. exponential stability of the θ-Euler-Maruyama method, including the linear growth condition on the drift coeffcient of the equation, are revealed. An example is provided to support the main results of the paper.

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